Instructor Insights pages are part of the OCW Educator initiative, which seeks to enhance the value of OCW for educators.
Instructor Insights
Below, Dr. Andrew Sutherland describes various aspects of how he converted 18.783 Elliptic Curves to an online course during the COVID-19 pandemic.
Note: Dr. Sutherland has also provided insights on teaching 18.783 in person in 2019.
OCW: What was your overall approach to redesigning the course for online teaching during the COVID-19 pandemic?
Andrew Sutherland: I used a combination of slides and hand-written proofs on paper using a document camera. Slides are good for summarizing facts and data, but hand-writing is better for detailed discussions, especially proofs.
I thought it would be useful to take advantage of the online medium to present additional content that I really couldn't present as effectively in class.
— Dr. Andrew Sutherland
OCW: How does allowing students to download your lecture slide files change the teaching-and-learning dynamic for you and your students? What do the lecture slides provide that the lecture notes don't?
Andrew Sutherland: The slides summarize content in a way that is easier to digest in real time than the lecture notes. Pretty much everything on the slides is also in the lecture notes—and if I were lecturing on a blackboard in a physical classroom, pretty much everything I wrote on the board would also be in the lecture notes.
OCW: You decided to include a bonus video (on root-finding and polynomial factorization) among the course materials for this iteration of 18.783. What was your motivation for creating this video, and how does it fit in with the rest of the material in the course?
Andrew Sutherland: I thought it would be useful to take advantage of the online medium to present additional content that I really couldn't present as effectively in class. Watching someone using a computer algebra system works better online, especially when you can follow along with your own copy of the notebook, try things for yourself, and pause the video whenever you need to.
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Curriculum Information
Prerequisites
A course in algebra covering groups, rings, and fields (including Galois theory) at the level of 18.701 Algebra I or 18.702 Algebra II.
Requirements Satisfied
18.783 can be applied toward a Bachelor of Science in Mathematics, but is not required.
Offered
Until this iteration of 18.783, the course was offered every other spring semester; due to increasing enrollment it is now offered every spring.
Assessment
Grade Breakdown
The grade was derived by averaging the student’s ten highest grades from among the twelve problem sets, with additional credit points given for participation in Zoom polls held in class.
Student Information
Breakdown by Year
About 3/4 advanced undergraduates, 1/4 graduate students.
Breakdown by Major
About 2/3 pure mathematics, 1/3 applied mathematics.
How Student Time Was Spent
During an average week, students were expected to spend 12 hours on the course, roughly divided as follows:
In Class
- Met 2 times per week for 1.5 hours per session; 26 sessions total; mandatory attendance.
- Several of the lectures included interactive sessions using Sage. The Sage worksheets are listed in the lecture notes section.
Out of Class
- There was no required textbook, but references to several books and articles were provided for each class session.
- The problem sets included both theoretical questions and practical examples that required the students to implement algorithms in Sage.